Unless there is something you are not saying I suspect (like the others) that she is just doing normal puppy play. A puppy plays with its siblings and parent by biting, tugging, pulling and so on, it is your job to teach her how to play in a way that is acceptable to you. It takes time, how much depends on the breed, your method, your consistancy and when you start.

Have you enrpolled her in puppy classes? the instrutors are often great people to talk to for ideas on certain behaviours.

She's drawn blood? Have you looked at those teeth? They are needle sharp, just running them across the skin in certain areas would draw blood without any pressure at all.

Your older dog probably will turn on her and tell her off, it is what they do to each other. He will turn and sy "ENOUGH" in his way and she will start to learn his boundareis. The fact that he hasn't done that already means he is obviously not as bothered by it as you!

Did you not research puppies? Or did you assume all dogs would be like your first?

my daughter bit me when she was 10months old and drew blood ,would you expect me to re-home her ? Fair enough if you find the dog too much to cope with ,but its hardly fair to blame the puppy for being a puppy

If you don't want her then it is a different question. What breed is she? Call a decent breed rescue and chat to them about it. Just please don't say "she is dangerous and keeps atacking the kids" tell them she is more boisturous than your previous puppy and you are not sure if it is aggressive but you cannot cope with it.

Other wise you are consigining her to a life she may not deserve, let the experts assess her.